Nuprl Lemma : le-add-cancel4
∀[c,t,t':ℤ]. uiff((c + t) ≤ t';c ≤ 0) supposing t = t' ∈ ℤ
Proof
Definitions occuring in Statement :
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
add: n + m,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
le: A ≤ B,
not: ¬A,
implies: P ⇒ Q,
false: False
Lemmas referenced :
le-add-cancel3,
less_than'_wf,
le_wf,
equal_wf,
zero-add
Rules used in proof :
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesisEquality,
natural_numberEquality,
independent_isectElimination,
hypothesis,
addEquality,
intEquality,
because_Cache,
isect_memberFormation,
introduction,
sqequalRule,
productElimination,
independent_pairEquality,
isect_memberEquality,
lambdaEquality,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
voidElimination
Latex:
\mforall{}[c,t,t':\mBbbZ{}]. uiff((c + t) \mleq{} t';c \mleq{} 0) supposing t = t'
Date html generated:
2016_05_13-PM-03_31_22
Last ObjectModification:
2015_12_26-AM-09_46_03
Theory : arithmetic
Home
Index